402.3B1 Open Sets in the Standard Metric Topology

Описание к видео 402.3B1 Open Sets in the Standard Metric Topology

What makes a subset of the real numbers an "open set" in the standard sense? Definition and a proof of the theorem that every finite open interval (a,b) is an open set. See the playlist: http://matthematics.com/real

0:00 Introduction and the "Horizon"
1:24 Motivation for Open Sets
2:15 Definition of Open Set, Three Ways
4:38 Open Intervals are Open Sets (Proof)
13:24 What Else Can There Be?

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